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Simplifying 2t2 + -11t + 7 = 0 Reorder the terms: 7 + -11t + 2t2 = 0 Solving 7 + -11t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -5.5t + t2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -5.5t + -3.5 + t2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -5.5t + t2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -5.5t + t2 = 0 + -3.5 -5.5t + t2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -5.5t + t2 = -3.5 The t term is -5.5t. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t + 7.5625 + t2 = -3.5 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = -3.5 + 7.5625 Combine like terms: -3.5 + 7.5625 = 4.0625 7.5625 + -5.5t + t2 = 4.0625 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (t + -2.75) equal to 2.015564437 and -2.015564437.Subproblem 1
t + -2.75 = 2.015564437 Simplifying t + -2.75 = 2.015564437 Reorder the terms: -2.75 + t = 2.015564437 Solving -2.75 + t = 2.015564437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = 2.015564437 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.015564437 + 2.75 t = 2.015564437 + 2.75 Combine like terms: 2.015564437 + 2.75 = 4.765564437 t = 4.765564437 Simplifying t = 4.765564437Subproblem 2
t + -2.75 = -2.015564437 Simplifying t + -2.75 = -2.015564437 Reorder the terms: -2.75 + t = -2.015564437 Solving -2.75 + t = -2.015564437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = -2.015564437 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.015564437 + 2.75 t = -2.015564437 + 2.75 Combine like terms: -2.015564437 + 2.75 = 0.734435563 t = 0.734435563 Simplifying t = 0.734435563Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.765564437, 0.734435563}
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